Question

Travis has a savings account that his parents opened for him. It pays 6% annual interest. His uncle also opened an account for him, but it pays 8% annual interest. If there is $500 more in the account that pays 6%, and the total interest from both accounts is $100, how much money is in each of the accounts?

Answer 1

So let's say the amounts are "a" and "b", at 6% and 8% respectively.

how much is 6% of a?  well (6/100) * a, or 0.06a.
how much is 8% of b?  well (8/100) * b, or 0.08b.

so hmm whatever "a" and "b" amounts are, we know that their yield is $100, thus 0.06a + 0.08b = 100.

now, there's more money in "a" than in "b", 500 bucks more, so whatever "b" is, we know that a = b + 500.

$\bf \begin{cases} 0.06a+0.08b=100\\ \boxed{a}=b+500\\ ----------\\ 0.06\left( \boxed{b+500} \right)+0.08b=100 \end{cases} \\\\\\ 0.06b+0.08b+30=100\implies 0.02b=70\implies b=\cfrac{70}{0.02} \\\\\\ b=3500$

how much was deposited in the 6% one?  well, a = b + 500.